Question

lincoln high wants to estimate the number of seniors who plan to go to a 4-year college. answer the following.
(a) which of the following surveys probably would best represent the entire population of seniors?
25 seniors are randomly selected; 14 plan to go to a 4-year college.
25 honor roll students are randomly selected from the senior class; 15 plan to go to a 4-year college.
25 glee club members are randomly selected; 16 plan to go to a 4-year college.
(b) there are 350 seniors at lincoln high.
using your answer from part (a), estimate the number of seniors who plan to go to a 4-year college.
seniors

Explanation:

Part (a)

To best represent the entire population of seniors, the sample should be random and unbiased. Selecting 25 seniors randomly (first option) is a simple random sample that includes all seniors, while the other options (honor roll students, glee club members) are biased samples (only from specific groups, not representative of all seniors).

Step 1: Find the proportion of seniors in the sample who plan to go to a 4 - year college.

The sample in part (a) has 25 seniors, 14 of whom plan to go to a 4 - year college. The proportion \(p=\frac{14}{25}\).

Step 2: Estimate the number of seniors in the entire population.

There are 350 seniors in total. Multiply the total number of seniors by the proportion: \(350\times\frac{14}{25}\).
First, simplify \(\frac{350}{25} = 14\), then \(14\times14=196\).

Answer:

A. 25 seniors are randomly selected; 14 plan to go to a 4 - year college.

Part (b)